Method of estimating short circuit current available by analysis of DC charging circuit

ABSTRACT

A system and method of dynamically estimating the short circuit current availability (SCCA) at a node in an alternating current electrical distribution system by examining the spectral composition of current drawn by a direct current charging circuit connected to the node. A correlative relationship between the total harmonic current distortion (THDi) in the current drawn by the charging circuit and the SCCA at the node is established for a particular charging circuit. An estimation of the SCCA at the node is accomplished by taking current measurements of current drawn by the charging circuit, analyzing those current measurements to determine the THDi, and estimating a corresponding value of SCCA based on the determined THDi. A method is also provided for calibrating a particular charging circuit to have a reactance and resistance suitable for use in estimating SCCA.

FIELD OF THE INVENTION

The present disclosure relates generally to estimation of arc flashhazard potential at a node in an electrical power delivery system, and,more particularly, to a system and method of dynamically estimating theshort circuit current availability at a node in an alternating currentelectrical circuit based on the total harmonic current distortion of thecurrent drawn by a direct current charging circuit also connected to thenode.

BACKGROUND

An arc flash event generally occurs when air is ionized to conductelectrical energy between two conductors that have a voltage potential.During an arc flash event, energy is released that may cause burns andother injuries to anyone or anything that is in proximity to the event.Under requirements from the Occupational Safety and HealthAdministration (OSHA), employers are required to categorize arc flashhazard potential in areas where workers are required to conduct work onor near live electrical equipment, and to provide proper guidelines onproper protective wear and safe working distances for their workers. Inorder to categorize the arc flash hazard potential, a detailed study ofthe electrical system is generally required to determine: the shortcircuit current availability, the distance from the power supplystation, the infrastructure connecting the particular node to the powersupply station, and details about the circuit breaker safety shut-offsand their response-time profiles.

Generally, the most costly parameter to estimate is the short circuitcurrent available (SCCA), which is a measure of the amount of currentthat can be drawn from a particular node in an alternating current (AC)electrical circuit in the event of a short-circuit event. Once anaccurate estimate of SCCA is made, determining the arc flash hazardpotential can be performed according to the methods provided in, forexample, publication 1584 of the Institute of Electrical and ElectronicsEngineers (IEEE 1584). Similarly, the arc flash hazard potentialcategory can be determined according to the methods provided in standard70E of the National Fire Protection Association (NFPA 70E). The arcflash hazard potential and arc flash hazard potential category can beused by workers to, for example, identify a safe working distance,select suitable personal protective wear, and to otherwise maintain asafe working environment. Typically, estimations of SCCA are made byconsidering the distance of the particular node from the powergeneration station, the nature of the transformers connecting theparticular node to the power distribution system supply wires, and thegauge and materials of the conductors connecting the particular node tothe transformers. But these methods may undesirably lead toover-estimates of SCCA.

Overestimates of SCCA can be dangerous and may lead to lower calculatedincident energy in the event of an arc flash than the risk that isactually presented, because many protective devices have inverse, orextremely inverse time-response curves such that a very high-current arcflash will trigger the protective device very quickly and result in lessincident energy than a relatively low-current arc flash that is allowedto endure for a longer duration due to the delayed reaction of theprotective device. It is desirable, therefore, to accurately estimateSCCA at a particular node in an AC electrical circuit. Furthermore, itis desirable to estimate SCCA dynamically, and in real time so as toprovide updated SCCA information as SCCA changes due to, for example,changes in the configuration of the power distribution system.

BRIEF SUMMARY

Provided herein is a method for estimating a quantity of short circuitcurrent available (SCCA) at a node in an alternating current (AC)electrical circuit. The present disclosure provides for analyzing thecurrent drawn by a direct current (DC) charging circuit connected to thenode in the AC electrical circuit. The current is analyzed to determinethe total harmonic current distortion (THDi). Aspects of the presentdisclosure provide for establishing a correlation between the determinedvalues of THDi and SCCA of the AC electrical circuit at the point ofmeasurement. Using the correlation between THDi of the DC chargingcircuit and the SCCA of the AC electrical circuit, implementations ofthe present disclosure provide a method for estimating a quantity ofSCCA based on the determined THDi.

Aspects of the present disclosure note that a plot of THDi against SCCAreveals two regions, or ranges of SCCA, with the two regions separatedby an inflection point. While the correlation in one region can bemodeled by a polynomial, the region beyond the inflection point is notas readily described mathematically. Methods are disclosed foradvantageously adjusting or tuning parameters of the DC charging circuitin order to maintain the correlation between THDi and SCCA in the regionof the correlation relationship that can be accurately modeled.Implementations of the present disclosure further provide fordynamically adjusting parameters of the DC charging circuit in order tomaintain the DC charging circuit in a region of the correlationrelationship that can be accurately modeled even as SCCA may changedynamically due to, for example, changes in the configuration of the ACelectrical circuit. Aspects of the present disclosure further providefor methods of using the estimate of SCCA to compute values of the arcflash hazard potential and arc flash hazard potential category andcommunicating that information.

The foregoing and additional aspects and implementations of the presentdisclosure will be apparent to those of ordinary skill in the art inview of the detailed description of various embodiments and/or aspects,which is made with reference to the drawings, a brief description ofwhich is provided next.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other advantages of the present disclosure will becomeapparent upon reading the following detailed description and uponreference to the drawings.

FIG. 1 is a flowchart providing an exemplary implementation of thepresent disclosure for estimating the short circuit current available ata node in an alternating current electrical circuit by measuring thetotal harmonic current distortion of current drawn by a direct currentcharging circuit connected to the node.

FIG. 2A provides an example configuration of a system for measuring thetotal harmonic current distortion of current flowing into a directcurrent charging circuit connected to a node of an alternating currentelectrical circuit.

FIG. 2B provides an example configuration of a system for measuring thetotal harmonic current distortion of current flowing into a directcurrent charging circuit removably connected to a node of an alternatingcurrent electrical circuit.

FIG. 2C provides an example configuration of a system for measuring thetotal harmonic distortion of current flowing into a direct currentcharging circuit useful for generating experimental results of therelationship between the total harmonic current distortion and shortcircuit current available.

FIG. 3 illustrates a chart showing experimental and simulation resultsdemonstrating the relationship between the total harmonic currentdistortion and short circuit current available.

DETAILED DESCRIPTION

FIG. 1 is a flowchart 100 providing an exemplary implementation of thepresent disclosure for estimating the short circuit current available(SCCA) at a node in an alternating current (AC) electrical circuit. SCCAis estimated by measuring the total harmonic current distortion (THDi)of current drawn by a direct current (DC) charging circuit connected tothe node. In an implementation, the current flowing into the DC chargingcircuit is measured with a current sensor to form a set of measurements.The THDi of the current flowing into the DC charging circuit isdetermined based on the set of measurements. An estimate of a quantityof SCCA is made based on an established correlation between the THDi inthe DC charging circuit and SCCA at the node of interest in the ACelectrical circuit. The flowchart 100 provides for the collection of aset of current measurements (110), analyzing those measurements todetermine the THDi (120), estimating a quantity of SCCA based on thedetermined value of THDi (130), and storing the estimate of SCCA in amemory (140). In an example configuration, the node of interest in theAC electrical circuit can be a point of common coupling (PCC) as thatterms is understood by those skilled in the art of power systems. Thenode of interest can be an access point where a user can access adisconnect and protective devices. The node of interest can also be apoint where, when permanently installed, a device such as a transformeris self-protected.

It should be emphasized that the term THDi and SCCA are used as thoseterms are commonly understood by those skilled in the art of powersystems. The lowercase “i” in THDi refers to current as opposed to othertypes of input waveforms that can be used to determine total harmonicdistortion. SCCA is a measure of the amount of current that can be drawnfrom a particular node in an alternating current (AC) electrical circuitin the event of a short-circuit event. THDi is typically expressed as apercentage or a ratio and SCCA is typically expressed in kilo-amperes(kA).

Following the estimating a quantity of SCCA based on the determinedvalue of THDi (130), an implementation of the present disclosure canoptionally calculate the arc flash hazard potential based in part on theestimated quantity of SCCA, for example, according to formulae providedin publication 1584 of the Institute of Electrical and ElectronicsEngineers (IEEE 1584). The arc flash hazard potential category canoptionally be determined, for example, according to the methods providedin standard 70E of the National Fire Protection Association (NFPA 70E).An implementation can communicate the determined SCCA, arc flash hazardpotential or arc flash hazard potential category by displaying theinformation on a user interface. The user interface can incorporate: adisplay, blinking lights, an audible alarm, or any other device suitablefor communicating information. Alternatively or additionally, animplementation can communicate the information by sending theinformation to a recipient. In a configuration, the communication of thedetermined SCCA, arc flash hazard potential or arc flash hazardpotential category can be performed when either exceeds, or drops below,a threshold value. Implementations of the present disclosure alsoprovide for communicating the estimated quantity of SCCA and forcommunicating an alert in the event that the estimated quantity of SCCAexceeds a threshold value. In an example configuration, the alert can becommunicated by displaying the alert information on a user interfacesuch as the user interface described above or by sending the alertinformation to a recipient.

FIG. 2A provides an example configuration of an SCCA estimation system200. The SCCA estimation system 200 includes an AC electrical circuit215 having a first line 210, a second line 212, and a third line 214. Inthe example configuration provided, the three lines (210, 212, 214) eachcarry voltage and current waveforms that are phase offset from theothers by 120 degrees. The three lines (210, 212, 214) are electricallyconnected to a DC charging circuit 220. Current delivered by the threelines (210, 212, 214) is measured with respective current sensors (230,232, 234) connected in series to the corresponding lines (210, 212,214). The current sensors (230, 232, 234) are also connected to acontroller 240. The controller 240 includes a processor 250 and a memory260. The controller 240 is configured to receive a set of currentmeasurements taken by the current sensors (230, 232, 234). Any of thecurrent sensors (230, 232, 234) can operate to measure the current drawnby the DC charging circuit 220 and report the current measurements tothe controller 240. The SCCA estimation system 200 is configured to usethe set of current measurements to form an estimate of a quantity ofSCCA at a node 205. The node 205 is a point on any of the three lines(210, 212, 214) where current is flowing to the DC charging circuit 220from the AC electrical circuit 215. The processor 250 is used by thecontroller 240 to determine THDi based on the set of currentmeasurements and to estimate a quantity of SCCA based on the determinedTHDi. The processor 250 can optionally be used by the controller 240 tocalculate an arc flash hazard potential according based on an estimatedquantity of SCCA and additional values that can be supplied by a user orsupplied by additional measurement devices. The processor 250 canfurther be used to correlate the arc flash hazard potential to an arcflash hazard potential category. The memory 260 is used by thecontroller 240 to store the set of current measurements received fromthe current sensors (230, 232, 234) and to store estimates of SCCA anddeterminations of THDi. The memory 260 can optionally be used to storethe arc flash hazard potential and the arc flash hazard potentialcategory.

The DC charging circuit 220 includes an inductor 222, a capacitor 224, aresistor 226, and a diode rectifier 270. The diode rectifier 270includes six diodes: a first diode 271, a second diode 272, a thirddiode 273, a fourth diode 274, a fifth diode 275, and a sixth diode 276.The three lines (210, 212, 214) of the AC electrical circuit 215 areconnected to the diode rectifier 270. The first line 210 is electricallyconnected to the anode of the first diode 271 and the cathode of thesecond diode 272. The second line 212 is connected to the anode of thethird diode 273 and the cathode of the fourth diode 274. The third line214 is connected to the anode of the fifth diode 275 and the cathode ofthe sixth diode 276. The anodes of the second diode 272, fourth diode274, and sixth diode 276 are connected to a first DC output 277 of thediode rectifier 270. The cathodes of the first diode 271, third diode273, and fifth diode 275 are connected to a second DC output 278 of thediode rectifier 270. In an implementation, the resulting configurationof the diode rectifier 270 can be referred to as a diode bridge. Thediode rectifier 270 can operate to rectify AC current from the ACelectrical circuit 215 into DC current in the DC charging circuit 220.The inductor 222, the capacitor 224, and the resistor 226 combine tosimulate the effect of a load on the DC charging circuit 220. Theinductor 222 is connected in series between the first DC output 277 andthe capacitor 224. The capacitor 224 is connected in series between theinductor 222 and the second DC output 278. The resistor 226 is connectedin parallel across the capacitor 224. In an example configuration, theDC charging circuit 220 can be used for experimental purposes toengineer the inductive, capacitive, and resistive parameters of the DCcharging circuit 220.

While the above configuration has been described using a diode rectifier270 to supply a DC current to the DC charging circuit 220, aspects ofthe present disclosure relate to similar systems incorporating anyrectifier circuit for supplying DC current from an AC current supply,including, for example, systems incorporating solid-state switchingarrays composed of six or more insulated-gate bipolar transistors.Configurations can optionally be implemented where the DC chargingcircuit 220 is connected to only two current-carrying lines of an ACelectrical circuit, or to one current-carrying line and a ground orneutral line of an AC electrical circuit. In an example implementationof the SCCA estimation system 200, the AC electrical circuit 215 can bean AC power delivery system, and the three lines (210, 212, 214) can bepower delivery lines. In a configuration, the node 205 where the currentsensors (230, 232, 234) are connected to the SCCA estimation system 200can be a point of common coupling (PCC) as that term is understood inthe context of power systems. Furthermore, while the SCCA estimationsystem 200 is illustrated with three current sensors (230, 232, 234), inalternate configurations, fewer or greater than three current sensorscan be present, such as one, two, or four. The current sensors (230,232, 234) can optionally be Hall Effect current sensors or current tovoltage transducers. In configurations incorporating more than onecurrent sensor, the controller 240 can analyze sets of currentmeasurements from each current sensor and can determine THDi from eachset of measurements and can consider the average THDi. A configurationof the SCCA estimation system 200 can also incorporate voltage sensorsto measure the voltage potential of the three lines (210, 212, 214). Thevoltage measurements can be used to calculate the arc flash hazardpotential or arc flash hazard potential category. Additionally, thevoltage measurements can be analyzed for spectral content, andinformation about the spectral content of the voltage waveform can beadvantageously used to further refine the determination of THDi byfiltering out imposed harmonic distortion in the waveform. DeterminingTHDi by utilizing spectral content information from the voltage waveformcan result in a more accurate estimation of SCCA.

The controller 240 is configured to analyze the current measurements todetermine the total harmonic current distortion (THDi) of the currentdrawn by the DC charging circuit 220. The controller 240 performs aspectral analysis of the measured current. The controller finds thecontent of measured current at the fundamental frequency of voltage orcurrent in the AC electrical circuit 215 and at selected harmonicfrequencies of the fundamental frequency. The controller 240 thendetermines THDi by computing the ratio between the measured current atthe selected harmonic frequencies and the fundamental frequency.Alternatively, the controller 240 can compute the THDi by determiningthe ratio of the measured current at selected harmonic frequencies tototal current. For example, the fundamental frequency of the voltage orcurrent in the AC electrical circuit 215 can be 60 hertz or 50 hertz,and the harmonic frequencies occur at integer multiples of thefundamental frequency. For example, the current sensors (230, 232, 234)can be configured to sample the current flowing into the DC chargingcircuit 220 at regular intervals at a rate of 250 kilohertz, or atanother rate suitable for analyzing the measured current at a desiredfrequency subject to the limitations of the Nyquist theorem. In the SCCAestimation system 200 illustrated in FIG. 2A, once the measured currentis received by the controller 240, digital signal processing techniquescan be employed to examine the measured current for its spectralfeatures. For example, the measured current can optionally be analyzedusing a fast Fourier transform, a discrete Fourier transform, or anyother method for computing the content of a measured signal atparticular identified frequencies.

In implementations of the present disclosure, the DC charging circuit220 can optionally be permanently connected to the AC electrical circuit215. For example, in a configuration where the AC electrical circuit 215is an AC power circuit, the DC charging circuit 220 can be an electroniccomponent incorporated into an electrical panel. In such an exampleconfiguration, the SCCA estimation system 200 is implemented bymeasuring the current drawn by the DC charging circuit 220 and analyzingthe set of current measurements with a controller 240. Inimplementations of the SCCA estimation system 200, the inductance,capacitance, and resistance of the DC charging circuit 220 can be due toan electronic component being powered by the DC charging circuit. Inimplementations of the SCCA estimation system 200, the inductance,capacitance, and resistance of the DC charging circuit 220 canoptionally be adjustable.

FIG. 2B provides an alternative implementation of the SCCA estimationsystem 200′ incorporating a DC charging circuit 220 that is removablyconnected to the AC electrical circuit 215. Referring now to FIG. 2B,the AC electrical circuit 215 has three lines (210, 212, 214), and eachis electrically connected to the DC charging circuit 220. The DCcharging circuit 220 is housed within a case 280. The case 280 hasconductive terminals (282, 284, 286) accessible from the exterior of thecase 280. The conductive terminals (282, 284, 286) are adapted to makean electrical connection with the three lines (210, 212, 214) of the ACelectrical circuit 215. The first line 210 is connected to a firstconductive terminal 282; the second line 212 is connected to a secondconductive terminal 284; and the third line 214 is connected to a thirdconductive terminal 286. The conductive terminals (282, 284, 286) areelectrically connected to the DC charging circuit 220 with conductors(281, 283, 285) housed within the case 280. The case 280 furtherincludes the current sensor 230, which measures the current drawnthrough the first line 210. The current sensor 230 is connected to thecontroller 240 and is configured to send a set of current measurementsto the controller 240. In the exemplary implementation provided only thecurrent drawn through the first line 210 is measured with the currentsensor 230 to provide a set of current measurements to the controller240, however implementations of the present disclosure may incorporatecurrent sensors measuring the current drawn through each of the threelines. In implementations where the DC charging circuit 220 is removablyconnected to the AC electrical circuit 215, the DC charging circuit canbe engineered to have a particular inductance, capacitance, andresistance suitable for estimating a quantity of SCCA at the node 205.The inductance, capacitance, and resistance of the DC charging circuit220 can optionally be adjustable. The SCCA estimation system 200′provided in FIG. 2B is shown with the controller 240 located outside ofthe case 280, but the present disclosure is not so limited. The case 280housing the DC charging circuit 220 can optionally house the controller240. The controller 240 is configured to use the processor 250 and thememory 260 to analyze the set of current measurements from the currentsensor 230 to determine THDi, and use an established correlation toestimate a corresponding value of SCCA of the AC electrical circuit 215at the node 205.

The SCCA at the node 205 of the AC electrical circuit 215 can beestimated based on the THDi of the current drawn by the DC chargingcircuit 220. The estimation is performed utilizing a correlationestablished between the quantity of SCCA at the node 205 and the THDi ofcurrent drawn by the DC charging circuit 220. The correlation betweenTHDi and SCCA for the DC charging circuit 220 can be establishedaccording to a method outlined below in connection with discussion ofFIG. 3. In brief, the correlation can be established by determining theTHDi when the DC charging circuit 220 is connected to a calibrated ACelectrical circuit 215 having a known value of SCCA. The SCCA of the ACelectrical circuit 215 can be modified and the THDi can be determinedrepeatedly until a correlation pattern is determined. Once a correlationpattern is established for the particular DC charging circuit 220,subsequent determinations of THDi can be used to estimate a quantity ofSCCA. The correlation between THDi and SCCA can optionally beestablished through computational simulation of an accurate electricalmodel of the DC charging circuit 220.

FIG. 2C provides still another example configuration of the SCCAestimation system 200″ useful for generating experimental results of therelationship between THDi and SCCA. The experimental results shown inFIG. 3 are generated using a configuration of the SCCA estimation system200″ shown in FIG. 2C. Referring now to FIG. 2C, the AC electricalcircuit 215 is implemented with an ATV61HD55N4 AC Drive three phasepower converter available from Schneider Electric. The current sensor230 is implemented with a Yokogawa PZ4000 Power Analyzer operating at asampling frequency of 250 kHz. The DC charging circuit 220 isimplemented having an inductance and capacitance matching the nominalvalues of the ATV61HD55N4 AC Drive three phase power converter. Theinductor 222 has a value of 0.12 mH, and the capacitor 224 has a valueof 3.9 mF. The value of the resistor 226 is selected to allow the ACelectrical circuit 215 to reach a power output of 79.8 kW. Accordingly,exemplary values of the resistor 226 for each of the experimentalresults are provided below in Table 1. While the AC electrical circuit215 includes three lines (210, 212, 214) connected to the DC chargingcircuit 220, in the exemplary implementation provided only currentflowing through the first line 210 is measured with the current sensor230. The first line 210 extending from the AC electrical circuit 215 isconnected to a first load resistor 292 and a first load inductor 291.Similarly, the second line 212 is connected to a second load resistor294 and a second load inductor 293, and the third line 214 is connectedto a third load resistor 296 and a third load inductor 295. The loadresistors (292, 294, 296) and the load inductors (291, 293, 295) combineto simulate an inductive load on the AC electrical circuit 215.

FIG. 3 illustrates an example chart showing experimental and simulationresults demonstrating a relationship between THDi and SCCA. The chartshown in FIG. 3 includes two sets of data. The square-shaped points areexperimental results gathered with the configuration of the SCCAestimation system 200″ shown in FIG. 2C. The diamond-shaped points aresimulation results determined by simulating the performance of the SCCAestimation system 200″ in a circuit simulation software program, namelySimulation Program with Integrated Circuit Emphasis (SPICE), which is ageneral-purpose open source electronic circuit simulator. Examination ofthe chart illustrated in FIG. 3 reveals two regions labeled Region 1 andRegion 2. In the particular configuration measured and simulated, Region1 corresponds to values of SCCA below roughly 30 kA, and Region 2corresponds to values of SCCA above roughly 30 kA. The point oftransition between Region 1 and Region can be described as an inflectionpoint 305, or informally as a “knee” in the correlation relationship. Aprecise mathematical description of the relationship between THDi andSCCA that spans both Region 1 and Region 2 may not be possible, but inRegion 1 the relationship can be modeled with a third order polynomial,and in Region 2 the relationship can be modeled as a logarithmicrelationship. In Region 1, the impedance of the AC electrical circuit215 dominates such that decreasing the impedance of the AC electricalcircuit 215 corresponds to greater generation of harmonic currents inthe DC charging circuit 220. The impedance of load inductors (291, 293,295) of the AC electrical circuit 215 is lower at larger values of SCCAas discussed below and shown in Table 1. According to the exampleconfiguration illustrated, changes in the impedance load inductors (291,293, 295) of the AC electrical circuit 215 in Region 2 do notsignificantly impact the generation of harmonic currents in the DCcharging circuit 220.

Referring again to FIG. 2C, adjusting the values of the load resistors(292, 294, 296) and the load inductors (291, 293, 295) allow for the ACelectrical circuit 215 to have specific values of SCCA at the node 205.To generate the experimental results shown in the chart illustrated inFIG. 3, the values were adjusted to provide the following SCCA values atthe node 205: 1 kA, 5 kA, 10 kA, 18 kA, and 22 kA. The values of theload resistors (292, 294, 296) and the load inductors (291, 293, 295)for each value of SCCA are provided below in Table 1. The reactance ofthe load for a frequency of 60 hertz is also provided in Table 1. Thesevalues were selected such that the power factor, the ratio of thereactance of the load to the load resistance, was 80% for each value ofSCCA generated. In Table 1 below, the leftmost column provides thevalues of SCCA generated by the AC electrical circuit 215 at the node205. The second column under the heading Rp provides the values of theload resistors (292, 294, 296); the third column under the heading Lpprovides the values of the load inductors (291, 293, 295). The fourthcolumn under the heading Xp provides the reactance of the AC electricalcircuit 215 at a frequency of 60 hertz. The fifth column under theheading R provides the values of the resistor 226 selected to allow theAC electrical circuit 215 to reach a power output of 79.8 kW for eachgenerated value of SCCA.

TABLE 1 Experimental SCCA Estimation System Values SCCA (kA) Rp (Ohm) Lp(mH) Xp (Ohm) R (Ohm) 1 0.222 0.441 0.166 5.38 5 0.044 0.088 0.033 5.5110 0.022 0.044 0.017 5.52 18 0.012 0.024 0.009 5.535 22 0.01 0.02 0.0085.55

The chart illustrated in FIG. 3 also provides results from a simulationof operation of the SCCA estimation system 200″ shown in FIG. 2C usingSPICE software. The simulation results appear as diamond-shaped pointson the chart illustrated in FIG. 3. The results of the SPICE simulationare gathered for each of the SCCA values measured experimentally.Additionally, simulation values of THDi are computed using SPICEsoftware for values of SCCA at 50 kA, 100 kA, and infinity. The finalthree simulation results are gathered, at least in part, to betterunderstand the behavior of the relationship between THDi and SCCA inRegion 2 as indicated in the chart shown in FIG. 3. For the final threesimulation results, the power factor, which is the ratio of the loadresistor 226 to the reactance of load at 60 hertz, is set to 20% ratherthan 80%.

Table 2 provides the results of the experimental results described aboveand displayed in the chart illustrated in FIG. 3. The values in Table 2include the content of the measured current at the fundamental frequencyand at selected harmonic frequencies. The value of THDi is alsoprovided. THDi is calculated by taking the square root of the sum of thesquares of the measured current at the selected harmonic frequencies anddividing by the measured current at the fundamental frequency. In Table2, the sum of the squares of the measured current at the selectedharmonic frequencies is also tabulated and referred to as I_(harm).Similarly, Table 3 provides the results of the simulation resultsdescribed above and displayed in FIG. 3.

TABLE 2 Experimental Results Harmonic 1 kA 5 kA 10 kA 18 kA 22 kAFundamental 108.22  103    110.03  109.48  109.78  5 30.17  48.03 63.43  67.53  69.54  7 7.49 23.94  36.25  41.02  42.76  11 2.69 3.783.84 3.89 4.28 13 0.93 1.45 2.21 2.16 2.21 17 0.18 0.37 0.36 0.37 0.4 19 0.12 0.16 0.22 0.18 0.2  23 0.03 0.08 0.07 0.07 0.07 25 0.02 0.040.06 0.04 0.03 29 0.03 0.02 0.01 0.01 0.01 31 0.01 0.02 0.04 0.02 0.03I_(harm) 31.21  53.82  73.19  79.14  81.77  THDi 29%  52%  67%  72% 74% 

TABLE 3 Simulation Results Harmonic 1 kA 5 kA 10 kA 18 kA 22 kA 50 kA100 kA Infinite Fundamental 131.29 127.4 129.6 130.83 130.88 130.83131.09 132.72  5 34.97 59.77 76.86 85.61 87.03 89.27 91.45 94.54  7 8.428.49 45.54 53.81 55.54 58.65 61.60 65.30 11 6.54 8.57 7.53 9.24 10.0212.07 13.92 16.32 13 4.1 5.89 8.89 8.76 8.47 8.29 7.90 7.75 17 1.96 4.263.96 5.16 5.6 6.44 7.10 7.77 19 1.84 2.73 3.66 3.5 3.48 3.82 4.22 4.8823 1 2.62 2.54 3.07 3.25 3.53 3.62 3.61 25 0.83 1.76 2.09 2.18 2.28 2.632.94 3.26 29 0.73 1.74 1.78 1.88 1.95 2.00 1.93 1.87 31 0.59 1.28 1.411.62 1.68 1.86 1.94 1.97 I_(harm) 36.91 67.32 90.35 102.21 104.39 108.2111.85 116.81 THDi 28% 53% 70% 78% 80% 83% 85% 88%

Once the correlation between THDi and SCCA is established for aparticular DC charging circuit, the correlation can be used to estimatea quantity of SCCA. This estimation can be performed in multipledifferent ways. For example, the estimation can be performed using alook-up table. A table of THDi values corresponding to quantities ofSCCA can be stored. When a present value of THDi is determined, thequantity of SCCA corresponding to a stored value of THDi closest orequal to the present value of THDi can be returned. Alternatively, aninterpolation of the values in the table can be performed. For example,when a present value of THDi is between two stored values of THDi in thetable, the corresponding calibrated quantities of SCCA can beinterpolated to return a quantity of SCCA intermediate to the valuesprovided in the table. In an example implementation, the interpolationcan be performed by using the controller 240 to compute a linearinterpolation, that is, a first order polynomial interpolation, of thecalibrated quantities of SCCA in the table corresponding to the twostored values of THDi closest or equal in value to the present value ofTHDi. Similarly, the interpolation can be performed by using thecontroller 240 to compute a second order polynomial interpolation of thecalibrated quantities of SCCA in the table corresponding to the threesaved values of THDi closest or equal in value to the present value ofTHDi. Similarly, the interpolation can be performed by using thecontroller 240 to compute a third order polynomial interpolation of thecalibrated quantities of SCCA in the table corresponding to the foursaved values of THDi closest or equal in value to the present value ofTHDi. In another example implementation, the estimation of a quantity ofSCCA can be performed by using the controller 240 to evaluate amathematical function at the determined value of THDi. The mathematicalfunction can be a third order polynomial that best fits the correlationdata according to any technique for fitting a mathematical function to aset of data. An implementation can provide a mathematical function thatdescribes the region of the correlation relationship with behaviorsimilar to that shown in Region 1 of the chart shown in FIG. 3.

As described above, the chart shown in FIG. 3 illustrates two regions inthe relationship between THDi and SCCA, Region 1 and Region 2. Region 1and Region 2 are divided by an inflection point 305. According to anaspect of the present disclosure, altering the values of the inductor222 or the capacitor 224 in the DC charging circuit 220 alters thelocation of the inflection point 305 such that a larger or smaller rangeof SCCA values are contained within Region 1. In an exampleconfiguration, the inductance or capacitance of the DC charging circuit220 are advantageously selected such that Region 1 spans a range ofvalues of SCCA that are anticipated to be present at the node 205 in theAC electrical circuit 215 that is sought to be monitored. As discussedpreviously, Region 1 corresponds to a range of values of SCCA wherechanges in the impedance of the AC electrical circuit 215 correspond tochanges in the harmonic current generation in the DC charging circuit220 that can be accurately modeled with, for example, a third orderpolynomial equation. Thus, by choosing values of the inductor 222 andthe capacitor 224 to give the DC charging circuit 220 a lower reactancethan the values utilized to generate the experimental resultsillustrated in the chart shown in FIG. 3, the inflection point 305 movesto the right such that a larger range of values of SCCA are contained inRegion 1. According to an aspect of the present disclosure, providing asmaller impedance or resistance for the DC charging circuit 220 allowsthe impedance or reactance of the AC electrical circuit 215 to dominateover a larger range than the example configuration that provided theexperimental and simulation results illustrated in the chart shown inFIG. 3 and provided in Tables 2-3.

The values of the inductor 222 and the capacitor 224 in the DC chargingcircuit 220 can be adjusted dynamically to maintain the relationshipbetween THDi and SCCA in a range that can be accurately modeled. Forexample, dynamically adjusting the values of the inductor 222 orcapacitor 224 can maintain the correlation relationship in a region thatis modeled with a third order polynomial, such as a region similar toRegion 1 in the chart illustrated in FIG. 3. In an example configurationthe inductance of the inductor 222 or the capacitance of the capacitor224 of the DC charging circuit 220 can be adjustable by the controller240 in response to an estimated quantity of SCCA exceeding a thresholdor falling below a threshold, or in response to a rate of change ofestimated quantities of SCCA exceeding a threshold or falling below athreshold. Alternatively, the inductance or capacitance of the DCcharging circuit 220 can be adjustable by the controller 240 in responseto determined values of THDi exceeding a threshold or falling below athreshold, or in response to a rate of change of determined values ofTHDi exceeding a threshold or falling below a threshold.

While particular implementations and applications of the presentdisclosure have been illustrated and described, it is to be understoodthat the present disclosure is not limited to the precise constructionand compositions disclosed herein and that various modifications,changes, and variations can be apparent from the foregoing descriptionswithout departing from the spirit and scope of the invention as definedin the appended claims.

What is claimed is:
 1. A method of estimating a quantity of shortcircuit current available (SCCA) at a node of an alternating current(AC) electrical circuit, the AC electrical circuit including a directcurrent (DC) charging circuit, the method comprising: electricallyconnecting the DC charging circuit to the node; measuring a currentflowing into the DC charging circuit to produce a set of currentmeasurements; determining a total harmonic current distortion (THDi)based on the set of current measurements; estimating a quantity of SCCAat the node based on the determined THDi, and on an establishedcorrelation between a known THDi and a known SCCA for the DC chargingcircuit; and storing the estimate of a quantity of SCCA in a memory. 2.The method of claim 1, wherein the estimating is performed by comparingthe determined THDi to a table of THDi values corresponding toquantities of SCCA and selecting the value of THDi closest or equal tothe determined THDi to reach an estimate of a quantity of SCCA.
 3. Themethod of claim 1, wherein the estimating is performed by comparing thedetermined THDi to a table of THDi values corresponding to quantities ofSCCA and interpolating the points in the table to reach an estimate of aquantity of SCCA.
 4. The method of claim 3, wherein the interpolating isperformed by computing a first order polynomial interpolation, a secondorder polynomial interpolation, or a third order polynomialinterpolation.
 5. The method of claim 1, wherein the estimating isperformed by evaluating a predetermined or calculated mathematicalfunction at a value of the determined THDi.
 6. The method of claim 1,the method further comprising: communicating an alert in the event theestimate of a quantity of SCCA exceeds a threshold value.
 7. The methodof claim 1, the method further comprising: estimating an arc flashincident hazard potential or an arc flash hazard potential categoryaccording to a function that includes the estimate of a quantity ofSCCA.
 8. The method of claim 7, the method further comprising:communicating an indication of the arc flash incident hazard potentialor the arc flash incident hazard potential category.
 9. The method ofclaim 1, wherein the DC charging circuit has a resistance, aninductance, or a capacitance and wherein the resistance, the inductance,or the capacitance is adjustable.
 10. The method of claim 9, the methodfurther comprising: responsive to the determining the THDi, adjustingthe resistance, the inductance, or the capacitance based on thedetermined THDi.
 11. The method of claim 1, the method furthercomprising: before electrically connecting the DC charging circuit tothe node: connecting a calibration circuit to the DC charging circuit;establishing, for the DC charging circuit, the established correlationusing the calibration circuit; disconnecting the DC charging circuitfrom the calibration circuit.
 12. A method of estimating a quantity ofshort circuit current available (SCCA) at a node in an alternatingcurrent (AC) electrical circuit, the method comprising: connecting adirect current (DC) charging device to the node, wherein the device hasa case that houses the DC charging circuit, the device further having aconductive terminal accessible from the exterior of the case; measuringcurrent flowing into the direct current charging circuit through theconductive terminal to produce a set of current measurements; analyzingthe set of current measurements to determine a total harmonic currentdistortion (THDi); estimating a quantity of SCCA at the node based onthe determined THDi; storing the estimate of a quantity of SCCA in amemory.
 13. The method of claim 12, wherein the case of the DC chargingdevice further houses a current sensor configured to measure currentflowing into the DC charging circuit, and wherein the device isconnected to a controller having a memory and a processor, and whereinthe controller is configured to receive current measurements from thecurrent sensor.
 14. The method of claim 12, wherein the estimating isperformed by comparing the determined THDi to a table of THDi valuescorresponding to quantities of SCCA and selecting the value of THDiclosest or equal to the determined THDi to reach an estimate of aquantity of SCCA.
 15. The method of claim 12, wherein the estimating isperformed by comparing the determined THDi to a table of THDi valuescorresponding to quantities of SCCA and interpolating the points in thetable to reach an estimate of a quantity of SCCA.
 16. The method ofclaim 15, wherein the interpolating is performed by computing a firstorder polynomial interpolation, a second order polynomial interpolation,or a third order polynomial interpolation.
 17. The method of claim 12,wherein the estimating is performed by evaluating a predetermined orcalculated mathematical function at a value of the determined THDi. 18.The method of claim 12, the method further comprising: estimating an arcflash incident hazard potential or an arc flash hazard potentialcategory according to a function including the estimate of a quantity ofSCCA.
 19. The method of claim 18, the method further comprising:communicating an indication of the arc flash incident hazard potentialor the arc flash incident hazard potential category.
 20. The method ofclaim 12, wherein the DC charging circuit has a resistance, aninductance, or a capacitance and wherein the resistance, the inductance,or the capacitance is adjustable, the method further comprising:responsive to the determining the THDi, adjusting the resistance, theinductance, or the capacitance based on the determined THDi.
 21. Amethod of estimating a quantity of short circuit current available(SCCA) at a node in an alternating current (AC) electrical circuit, theAC electrical circuit having a direct current (DC) charging circuit, themethod comprising: electrically connecting the DC charging circuit tothe node; measuring current flowing into the DC charging circuit toproduce a set of current measurements; analyzing the set of currentmeasurements to determine a total harmonic current distortion (THDi);estimating a quantity of SCCA at the node based on the determined THDi;measuring a voltage potential of the AC electrical circuit at the node;estimating an arc flash incident hazard potential or an arc flash hazardpotential category according to a function including the estimate of aquantity of SCCA and the measured voltage potential; and storing theestimate of the arc flash hazard potential or the arc flash hazardpotential category in a memory.